run php script with ajax shows no result

I'm trying to run a php script using ajax after a form submission. this is the form

<form id="form" class="form">
    <input id="email" type="email" required name="email" placeholder="Email" onchange="myUpdateFunction()" value="">
    <textarea id="message" type="text" value="" name="message" onchange="myUpdateFunction()" required placeholder="Comments" style="border:none;border-bottom:1px solid #424242; width:530px;"></textarea>
    <input id="submit" type="submit" class="submit" name="send_request" value="Submit" >
</form>

this is my script

$('.submit').on('click', function() {
        $.ajax({
          url: "send.php",
          method:'post',
          data: {'email': $('#email').val(), 'message': $('#message').val()}
        }).done(function() {
            alert('Message Sent.');

        });
   });

and this is my send.php file

<?php 

if(isset($_POST['send_request'])){
    //send email
}

?>

but it doens't work, the page is reloaded, the email is not sent and no "alert message" is displayed