Praise be to Allah.
Items that are solid and smooth (impermeable) may be purified by wiping them, according to the correct view, which is the view of Malik and Abu Hanifah, because what matters is removing the impure substance.
Al-Kasani (may Allah have mercy on him) said in Bada’i‘ as-Sana’i‘ (1/85):
If an impure substance (najasah) gets onto something that is solid and smooth (impermeable), such as a sword, mirror and the like, it may be cleansed by scratching, whether it is wet or dry, because none of the impurity will seep through it, and its surface may be cleansed by wiping and scratching. End quote.
Ad-Dasuqi al-Maliki said in al-Hashiyah ‘ala ash-Sharh al-Kabir (1/77): Conclusion: in the case of anything that is solid and smooth (impermeable), when there is the fear that it may be damaged by washing, such as a sword and the like, what got onto it of permissible blood, even if there is a large amount, may be overlooked, for fear of damaging it by washing it. End quote.
An-Nawawi (may Allah have mercy on him) said in al-Majmu‘ (2/599): If the impure substance (najasah) gets onto something solid, like a sword, knife, mirror and the like, it cannot be cleansed by wiping and can only be cleansed by washing like other things. This was the view of Ahmad and Dawud. Malik and Abu Hanifah said: It may be cleansed by wiping. End quote.
Shaykh Ibn ‘Uthaymin said:
In the case of things from which the impure substance may be removed by rubbing – which is items that are smooth, such as mirrors and swords, which do not absorb impurity – the correct view is that they may be purified by rubbing.
So if the mirror becomes contaminated with an impure substance, then it is rubbed until it becomes clear, with no impurity on it, then it has been purified."(Ash-Sharh al-Mumti‘ 1/426).
If the impure substance gets onto cushions and large furnishings such as rugs and the like, then the way to purify them is by pouring water on the impure spot, until the water overwhelms the impure substance that got onto it. Then the water that is contaminated with the impure substance should be dried up with a sponge or some other tool or machine. If the impure substance is removed by that means and no trace of it remains, then this is the desired outcome. If it does not disappear, then it must be washed a second or third time, until you think it most likely that it has been removed. There is no stipulation that the water used should be two or three times the amount of the impure substance, and the like.
It is not essential to wring out the impurity or to rub it, so long as the impure substance has disappeared.
Please see the answer to question no. 213577 .
There is no religious text which states the number of times impurity must be washed, except the impurity of a dog only, which must be washed seven times, one of which should be with dust. As for other kinds of impurity, no specific number is specified; rather it must be washed until the impure substance disappears, even if that is achieved by washing it only once.
See the answer to question no. 163825 .
What matters with regard to water by means of which an impure substance is removed is that it should be a copious amount, so that it will remove the impure substance and leave no trace of its colour or smell, without specifying a particular amount.
Ibn Qudamah (may Allah have mercy on him) said in al-Mughni (1/75), regarding purifying impurity other than that of a dog or pig, and whether washing it a specific number of times is required: There are two reports – meaning from Imam Ahmad – regarding that. The first report says that there is a stipulated number of times for that, by analogy with the impurity of a dog… The second report says that there is no stipulated number of times; rather it is sufficient to pour a great deal of water [on the impure substance], without counting a specific number of times, until the impurity is removed. This is the view of ash-Shafa‘i. End quote.
After researching the matter, we have not come across any statement by any scholar to suggest that it is sufficient for the water to be three times the amount of the impure substance. What appears to be the case is that that would not be sufficient, and that this amount of water would be contaminated by the impure substance and would change as a result.
What we found is that some of the scholars stipulated that in order to purify the ground of impurity, the water must be seven times the amount of the impure substance.
This view is more likely to be correct than the previous view, yet it is a weak view too, and we do not know of any evidence to indicate that it is sound.
An-Nawawi (may Allah have mercy on him) said: What is required in order to remove impurity that has seeped into the ground is to pour a large amount of water, so that the impure substance will be absorbed into it.
And there is a view which stipulates that the water that is poured on the ground should be seven times the amount of the urine.
This is a weak view; the correct view is the first one."(Al-Majmu‘ 2/611).
Based on that, what matters is that the water should be of a large amount, so as to remove the impurity, without specifying a particular amount of water.
The more correct scholarly view is that if impurity falls into water, it does not become impure unless it is changed thereby, such as if its colour or smell is changed.
This is the view of the Malikis, and is mentioned in one report from Imam Ahmad. It was regarded as more correct by Shaykh al-Islam Ibn Taymiyah and his student Ibn al-Qayyim. It is also the view favoured by many contemporary scholars, such as Shaykh Ibn Baz, Shaykh Ibn ‘Uthaymin, and the scholars of the Permanent Committee for Ifta’ (may Allah have mercy on them).
Please see the answer to question no. 224923 .
Based on that, if the impure garment is put in the bathtub and does not change the water that is in it, then the water remains pure and does not become impure thereby. But if the colour or smell of the water is changed by the impurity, then it becomes impure.
But whatever the case, you should not place the impure garment into a tub of water, if possible; rather you should wash off the impurity first, or pour water over it, so as to ward off any intrusive thoughts and so as to take into consideration the scholarly view which says that the water becomes impure thereby.
If the impure garment is washed in a washing machine and the trace of impurity is removed from it, then it becomes pure thereby.
Please see the answer to question no. 163825 .
With regard to your question about detergents and what they may contain of ingredients derived from impure animal sources, this is subject to further discussion:
If these detergents are obtained from animals which are impure, but after being processed and treated they turn into different substances with characteristics different from those of the impure source from which they were extracted, then there is nothing wrong with using them and cleaning things with them.
But if they have not undergone a complete transformation – rather they have retained some of the characteristics of the impure source from which they were obtained – then it is not permissible to use them, because they are part of something impure.
So long as we are not certain whether these impurities are present or not, the basic principle regarding these products is that they are pure and halal, and we should not open the door to intrusive thoughts, doubts and hardship.
In most cases, that which is derived from animals that were not slaughtered in the prescribed manner and animals that are not permissible to eat will have been transformed from its original state and will have been purified by this transformation. Therefore we may use such things without needing to pay attention to any of that.
Please see answer to question no. 97541 .
And Allah knows best.